Let a point P be such that its distance from the point (5,0) is thrice the distance of P from the point (-5,0) . If the locus of the point P is a circle of radius r, then 4 r 2 is equal to.

Question

Let a point P be such that its distance from the point (5,0) is thrice the distance of P from the point (-5,0) . If the locus of the point P is a circle of radius r, then 4 r 2 is equal to. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Let point is ( h , k ) So,√( h -5)2+ k 2=3 √( h +5)2+ k 2 8 x2+8 y2+100 x+200=0 x2+y2+(25/2) x+25=0 r2=((25)2/42)-25 4 r 2=(252/4)-100 4 r2=156.25-100 4 r 2=56.25 After round of 4 r2=56

Q. Let a point P be such that its distance from the point (5,0) is thrice the distance of P from the point (-5,0) . If the locus of the point P is a circle of radius r, then 4r2 is equal to_________.

Let point is (h,k) So,(h−5)2+k2​=3(h+5)2+k2​ 8x2+8y2+100x+200=0 x2+y2+225​x+25=0 r2=42(25)2​−25 4r2=4252​−100 4r2=156.25−100 4r2=56.25 After round of 4r2=56

Q. Let a point $P$ be such that its distance from the point (5,0) is thrice the distance of $P$ from the point (-5,0) . If the locus of the point $P$ is a circle of radius $r$ , then $4 r^{2}$ is equal to_________.